Which among the following salt turns blue litmus red in its aqueous solution?

Identification of acidic salt

The salt that turns blue litmus red must yield an acidic aqueous solution through hydrolysis of its constituent ions.

Copper(II) sulfate ($\mathrm{CuSO4}$) dissociates into $\mathrm{Cu^{2+}}$ and $\mathrm{SO_4^{2-}}$ ions. The $\mathrm{Cu^{2+}}$ cation, being the conjugate acid of weak base $\mathrm{Cu(OH)_2}$, hydrolyzes:
$\mathrm{Cu^{2+} + 2H_2 O <=> Cu(OH)_2 + 2H+}$
This reaction produces hydrogen ions, acidifying the solution.

Sodium carbonate ($\mathrm{Na_2CO_3}$) yields basic solution due to $\mathrm{CO_3^{2-}}$ hydrolysis: $\mathrm{CO_3^{2-} + H_2 O <=> HCO_3- + OH-}$.

Sodium sulfate ($\mathrm{Na_2SO_4}$) and sodium nitrate ($\mathrm{NaNO_3}$) form neutral solutions as both ions derive from strong acid-base pairs and undergo negligible hydrolysis.

$\mathrm{CuSO_4}$ is the only salt producing acidic solution that turns blue litmus red.